Braille Mathematical Notations

Various Braille codes for mathematics have been developed in different countries. Here is the information I collected about existing Braille Mathematical Notations. This is not complete. If you have any information which could help, please post a comment down here or to this blog entry.

The biggest source of information was the survey done by UNESCO and published in 1990 [1].

Mathematical and/or Scientific Braille notations

France

The Braille Mathematical code was ﬁrst adapted to Mathematics in 1922 by Louis-Auguste Antoine. Antoine was teaching Mathematics in secondary school until 1914 when he was mobilized. He became blind after being wounded at the face. After the war he adapted the Braille code to Mathematics and presented a PhD. Then he became professor at University of Rennes.

This code was revised a ﬁrst time in 1971. It was then deeply revised in 2001, in the goal of improving the collaboration between sighted and blind and facilitating automatic transcription. Another revision was done in 2007.

According to [1], in 1990 this code was also used in Madagascar and in Portugal.

Marburg

Marburg is used in German speaking countries. It was designed in 1955 in the Marburg school for the Blind in Germany by Helmut Epheser, Karl Britz and Friedrich Mittelsten Scheid. A heavily reworked and revised edition was published in 1986.

This code is at least used in Germany, Austria and Poland (with minor variations). According to [1], in 1990 it was also used in Denmark, The Netherlands, Norway and former Yougoslavia.

British Braille

The British notation is used in United Kingdom and in Ireland. It was ﬁrst designed in 1970, and a deeply revised version was published in 1987. This was slightly revised in 2005.

According to [1], in 1990 this code was used (various releases according to the different countries) in Australia, Barhein, Hong-Kong, Iran, Ireland, Jordan, Kenya, Nigeria, Saudi Arabia, Sierra Leone, Singapore, UK and Zimbabwe.

Nemeth

The Nemeth Code for Braille Mathematics was published and accepted as the standard code for representing math and science expressions in Braille in 1952. It was designed in 1946 by Abraham Nemeth so that he could complete his PhD in mathematics. The 1972 revision is the current official code in use in the US. Note that Nemeth was adopted in a number of Southeast Asian countries (like India, Thailand, Malaysia, Indonesia, Cambodia, Vietnam).

According to [1], in 1990 this code was also used in Canada, India, Iran, Israel, Lebanon, New Zealand, Pakistan, Saudi Arabia, Sri Lanka, Thailand, USA and Western Samoa.

The Nemeth Braille code for Mathematics and Science notation, 1972 revision, by A. Nemeth. American Printing House for the Blind, USA. 1972

Greece is using an adaptation of the Nemeth code, where the roles of Roman letters and Greek letters are in a sense reversed. Here is a document, in Greek, about the merits of Nemeth code, and the decription of the Nemeth code for Greece:

Unified English Braille

The International Council on English Braille is developing a Unified English Braille which was implemented yet in 4 countries: Australia, New Zealand, Nigeria and South Africa. The UEB Mathematics Committee is completing the assignments of symbols for technical materials and any rules necessary for their use.

Older information: [1] (1990) states that a unified code was approved by the « Conferencia Iberoamericana para la Unification del Sistema Braille » in Buenos Aires. 3 documents which seem to be different releases of this code are mentionned by different countries:

Japanese Mathematical Braille

The current Japanese Mathematical Braille notation was published in 2001 by the Japan Braille Committee. It is an important revision of the 1981 formal speciﬁcation of Japan Mathematical Notation, itself based on the notation published in 1956 by Japan Braille Research Group (“Nihon Tenji Kenkyukai”).

Bharati Braille Code for Mathematics (India)

Bharati Braille Code for Mathematics, by National Association for the Blind. National Association for the Blind. Bombay, 1978

The Netherlands

A set of rules, inspired by the Marburg code, was set up in the Netherlands in 1983.

A revised version of the notation in use was released by Dedicon in October 2009 . Information is available at wiskunde.dedicon.nl (in Dutch – the site provides lots of examples). The new version is closer to the notation used in the printed copy of a book. That way it facilitates understanding and cooperation between for instance a sighted teacher and a non-sighted student when both using a computer. Another consideration taken into account regarded best practices from (international) notation used when linearizing math for computer purposes, e.g. in spreadsheets, calculating software or even plain e-mail traffic.

Woluwe code

The Woluwe code was developed in the sixties for the Dutch speaking part of Belgium. It is based on the Marburg code. The developer of the Woluwe code was a former teacher at the Royal Institute for Deaf and Blind people (Koninklijk Instituut Woluwe), in Sint-Lambrechts-Woluwe, a suburb of Brussels.

System of Symbols for Math, Physics, Chemistry, and Astronomy: A Learning Aid, by A. G. Bykov, M.I. Egorov, F.B. Morozova and I.V. Proskurjakov. Edited by Proskurjakov and Bykov. Committee fr Exact Sciences for All Russia Association for the Blind. 2nd ed, rev and enl. The All Russia Association for the blind. Moscow, 1982.

According to [1], in 1990 this code was also used in Bulgaria, former Czechoslovakia (and I guess now Czech republic and Slovakia), and Denmark.

Czech republic

Other notations

HRTeX

HRTeX (Human Readable TeX) is a code developed at the Johannes Kepler Universität Linz, Austria, with the intention to supply teaching materials in a way more easily readable than TEX or LATEX. HRTeX is derived from TeX, although not compatible with it. These are some of the most important differences:

Many symbols are abbreviated. For instance, the symbols for Greek letters are composed of the ﬁrst two characters, e.g., al instead of alpha, be instead of beta, etc.

The names of standard functions are written like variables, but in upper case letters, e.g., SIN instead of sin, LOG instead of log, etc.

Alternative notation for fractions: The fraction bar is represented by two slashes – // -, and the whole fraction is written as a group. For instance, {a+b // c+d} instead of frac{a+b}{c+d}.

AMS

The ASCII Maths Notation (AMS) has been developed in University of Karlsruhe by Mr Schönberg in 1993. It uses exclusively the 128 characters of the 7-bit standard ASCII, which makes it platform independant. AMS is used in Germany, Austria and some eastern european states.

Lambda

Lambda is a mathematical reading and writing system designed for blind students. The software was developed in a pro ject of the same name, whose meaning is in full: “Linear Access to Mathematics for Braille Device and Audio Synthesis”. The Lambda software is mostly referred to as the “Lambda Editor” – it is an editor that enables a blind student to input and to edit mathematical expressions in a rather comfortable way.
The main characteristics of the Lambda pro ject is that it is built on a brand new code. This code is an XML code speciﬁcally designed for supporting the Braille transcription into 8-dot pattern national codes. Each Lambda national code has the lambda structure and a Braille character dictionary as close as possible to the official national code.

visual presentation in a linear code (a speciﬁc font in which each Braille character is represented by a visual symbol)

graphical rendering – not synchronous to input, the graphical rendering is built when the user presses a key. This view is then static. The graphical view is obtained by conversion of the Lambda code to MathML.

One Response to “Braille Mathematical Notations”

Unified English Braille has now been adopted by eight English-speaking countries: Australia, Canada, Ireland, New Zealand, Nigeria, South Africa, United Kingdom, United States. See http://www.iceb.org.